The Effect of Implant Length and Diameter on Stress Distribution of Tooth-Implant and Implant Supported Fixed Prostheses: An In Vitro Finite Element Analysis Study

The application of dental implant restorations to rehabilitate oral edentulism has increased in recent years.^1–3  Combining implants with natural dentition has been used by several practitioners as an alternative method of treatment rather than 2 implants supporting fixed partial denture (FPD). Various clinical studies have also investigated the possibility of a connection between the dentition and osseointegrated implants in cases where an implant placement is unattainable due to anatomical or financial limitations.^4–7 

As a whole, alveolar bone condition and bone volume both dictate the design and method of implant placement and help predict implant success.⁸  However, implant dimensions are also important predictors for success.⁹  Anitua et al¹⁰  conducted a finite element analysis (FEA) on the relation of implant dimensions and geometry to force dissemination, the results of which revealed that dissemination of force was mainly affected by the width of the implant rather than its length or geometry. The collar and the first 6 threads of the implant displayed the most force. Thus, the adoption of broader implants is consistently better for stress dissipation, and the application of wideshort implants presents a legitimate choice for the treatment of residual ridges of reduced alveolar height.

Additionally, Pierrisnard et al¹¹  using FEA assessed the relation of stress transmission to the implant and surrounding bone with respect to implant length and the quality of bone. In the 3D model, implants had the same diameter but different lengths. Implants were supported by 2 types of bone: cancellous and cortical. The model was tested under a 100-N load force on the prosthesis occlusal surface with buccolingual angulation of 30°. The subsequent results indicate that the length of the implant has no direct relation to force distribution.

Recently, Porrua et al¹²  studied a new dental implant using FEA by investigating the relation of its dimensions and elastic modulus to Von Mises equivalent stress (VMES) and strain (VMS) values of the surrounding bone. They conclude that the implant dimensions affected statistically the VMES and VMS values of the surrounding bone.

The FEA is an interpretive approach to testing the stress and strain of internal structures using a simulation model. It was established in the 1960s to clarify questions in different fields such as aerospace industry, electromagnetics, and engineering, and has recently been used in dentistry, dental mechanics, and dental implants.¹³ 

Essentially, finite element models are divided into triangles or rectangles, and their corners are termed as nodes. These shapes are described by the tested material, physical, and mechanical properties, as well as by their elastic modulus and Poisson's ratio (Table 1).¹⁴  By applying different loads to the simulating models, stress and strain at the nodes can be computed by algebraic equations. The computed outcome appears in terms of deformation, strain, and force within the model at the nodal points, or by VMES,¹⁵  which was not used to evaluate the implant diameter and length for different retained fixed restorations. The aim of this research was to appraise the effectiveness of the diameter and height of implant on force dissemination of tooth-implant and implant retained fixed restorations.

In the current investigation, a 3D simulation of 1 side of a mandibular Kennedy Class I bilateral edentulism case was constructed from a computed tomography (CT) input with DICOM format (digital imaging communication on medicine) processed through a Mimics software program. To construct this model, a volunteer patient was selected to undergo a mandibular CT scan. The patient was a male aged 32 years who had no developmental abnormalities nor gross defects, and had not undergone any previous surgery (Figure 1a). The study was approved by the ethics committee at King Abdulaziz University Faculty of Dentistry (KAUFD) (143-10-19).

A DICOM format was adopted using a Toshiba multisegment CT to obtain a CT illustration. The CT scan images were then exported to Mimics 8.1 program (Materializes Interactive Medical Image control system software: Mimics 8.1 for Intel × 86 Pentium III + V8.5.0.23) with initialization of anterior and posterior position for the axial plane and top and bottom position for the other planes.

Through thresholding the resultant assembly, a region of interest (ROI) was selected from the CT scan. A range of 578–3071 Hounsfield units was used to select the bone and teeth and the 3-unit restoration. Using the regional growing option, the mandible with the teeth was separated from the other structures in a new mask of a different color. The teeth were then extracted from the mandible and given a new mask (Figure 1b).

The 3D model was then calculated and obtained using the software's measured distance tool to assist in drawing and exporting the model to the Solidworks software program with IGES format (Solidworks Premium 2012 × 64 Edition: an engineering drawing program and finite element analysis; Solidworks Corporation).

Details of the diameter (D) and length (L) of implant were entered in the software. Ds used were 3.7, 4.7, and 5.7, while Ls used were 10, 11.5, and 13. The constant was the use of rigid connectors in both designs (implant-implant and implant-tooth FPDs) and the mesial implant (D 3.7 and L 11.5) (Figure 1c–e).

The periodontal ligament was simulated by the root of 0.2 mm. First the premolar and then the 3-unit restoration were imported and processed using the Mimics software program and converted with Rapidform XOS (mesh-to-solid software) to create a solid 3-unit restoration model (Figure 1f).

Consequently, the constructed components were assembled together to form 10 models that were divided into group A (tooth-implant FPD) and group B (implant-implant FPD). The technique of each model assembly depended on the mating function of the assembly mode in the Solidworks software.

The mating was accomplished between the compact bone to the spongy bone (compact, spongy bone complex) (Figure 1g); the premolar to its periodontal ligament; the periodontal ligament of the premolar to the compact, spongy bone complex; the implants to the compact, spongy bone complex, the abutment, the implant screw, and the implant itself; the metal framework of the restoration to second premolar (Figure 1h); and the metal framework of the restoration to the mesial and distal implants.

Another important step was defining the material properties for each component by assigning the moduli of elasticity and Poisson's ratios to each material used in the FEA (Table 1). The next step was to define contacts and gaps between FPD components, meaning that bonded contacts between 2 contacting surfaces along the interface are displayed as 1 unit upon load application. Subsequently, a force of 100 N was exerted over the central fossa of the bicuspids and cuspids of the 3-unit restoration for each of the 10 models (Figure 1i).

The final step before running the analysis was meshing the models, which is the process of subdividing the geometric model into small pieces called elements, which are connected at common points called nodes. A 3D curved tetrahedral solid fundamental was designed by a distinctive network. The coordinate parameters are represented (Figure 1j and k).

The FEA was executed by Solidworks Premium 2012 × 64 Edition. The governing matrix equations of the program were incorporated. The output of the analysis program was in the form of displacement (X-direction was mesiodistally, Y-direction was vertically, and Z-direction was anteroposteriorly) as well as stresses (a total of 6 stresses acted on each node; 3 normal and 3 shear stresses measured in MPa and presented as different colored contoured bands), along with the principal and VMES (Equivalent stress; Seqv (l/⁠) [(S1- S2)2 + (S2- S3)2+ (S3- S1)2]1/2). This process was performed for all loading conditions, and for each model, stresses were measured for each component: stresses in; (1) FPD, (2) the distal implant, (3) the second premolar, (4) cancellous bone around second premolar, mesial implant, and distal implant.

The data were illustrated as mean ± SD and was interpreted using Version 23 of SPSS Statistics for Windows by IBM (IBM Corp, Armonk, NY). Statistical comparisons between groups were made by unpaired Student t test. Strength and direction of association between the variables was computed using Pearson correlation.

Data were graphically represented as bars and charts using Prism Version 7. Results' significance was calculated at 5% level where P < .05.

Ten 3D pattern simulations of 1 side for a mandibular Kennedy Class I were constructed based on the methodology. Patterns were sorted into 2 groups based on their different diameters and lengths. The first group represented tooth-implant supporting FPD with rigid connection (Figure 2a–e). The second group represented implant-implant supporting FPD with rigid connection (Figure 2f–j).

Stresses within different designs calculated for different diameters and lengths in groups A and B are shown in (Table 2) (Figure 3a and b). Stresses in cancellous bone around mesial abutment (second premolar) in tooth-implant FPD and mesial implant in the implant-implant FPD revealed that the stress was significantly lower in tooth-implant FPD compared with implant-implant FPD (Table 3) (21.1 ± 0.00 vs 46.1 ± 0.00, P < .001). There were insignificant differences between other measured parameters between groups A and B (Table 3) (Figure 3a and b).

A statistically notable inverse correlation was noted among the diameter of the any implant and stresses. A decrease in stresses induced in distal implant and in cancellous bone around these distal implant were allied with an increase in implant diameter (r = −0.977, P < .001 and r = −0.510, P = .021). On the other hand, a statistically significant direct relation between implant length with stresses induced in distal implant, and in cancellous bone around these distal implants (r = 0.631, P = .003 and r = 0.795, P < .001, respectively) (Table 4).

The optimal combination of implant diameter and length was 5.7 and 10 mm, as it recorded the fewest stresses around the distal implant; conversely, the combination of 3.7–10 mm recorded the highest stress, and was hence the least favorable. This was true for both implant-implant and tooth-implant FPD designs (Figure 1c–h).

In the present study, the highest stresses were recorded in the model with a distal implant size of 3.7 mm diameter × 10 mm length (217 516 MPa); the second highest stresses were recorded in the model with a distal implant size of 4.7 mm diameter × 10 mm length (96 432 MPa) and a 55.6% decrease in stress. The lowest stresses were recorded in the model with a distal implant size of 5.7 in diameter × 10 mm length (45 132 MPa) and a 79.2% decrease in stress. Stress in cancellous bone around the distal implant had the same pattern from highest to lowest stresses with 46 0574 MPa, 43 6501 MPa (5.22% decrease in stress), and 40 1753 MPa (12.77% decrease in stress), respectively. Moreover, FPD had the same stresses and the highest stresses was with a distal implant size of 3.7 mm diameter × 10 mm length (387 9950 MPa); followed by a distal implant size of 4.7 mm diameter × 11.5 mm length (249 0570 MPa) and a 35.81% decrease in stress. The lowest stresses were a distal implant size of 5.7 mm in diameter × 10 mm length (222 0840 MPa) and a 42.76% decrease in stress.

The implant length has the same pattern as implant diameter regarding the distal implant and cancellous bone around these implants. The highest stresses were recorded in the model with a distal implant size of 3.7 mm diameter × 13 mm length (231 214 MPa); the second highest stresses were recorded in the model with a distal implant size of 3.7 mm diameter × 10 mm length (217 561 MPa) and a 5.9% decrease in stress. The lowest stresses were recorded in the model with a distal implant size of 3.7 mm in diameter × 11.5 mm length (204 496 MPa) and an 11.55% decrease in stress. The difference between the lowest and the second lowest stresses recorded was only 6.005%. Stress in cancellous bone around the distal implant had the same pattern from highest to lowest stresses with 64 3762 MPa, 46.0574 MPa (28.4% decrease in stress), and 45 7488 MPa (28.9% decrease in stress), respectively. The difference between the lowest and the second lowest stresses recorded was only 0.67%. Moreover, FPD had the same stresses and the highest with a distal implant size of 3.7 mm diameter × 10 mm length (387 9950 MPa); followed by a distal implant size of 4.7 mm diameter × 11.5 mm length (343 3430 MPa) and a 11.51% decrease in stress. The lowest stresses were a distal implant size of 3.7 mm in diameter × 13 mm length (240 5360 MPa) and a 38.01% decrease in stress.

Connecting natural teeth to implants is a controversial topic and produces a biomechanical challenge. This difficulty stems from the nature of each: the rigidity of dental implant to the bone and the resilience of the tooth due to the periodontal ligament.^16–19  While several rigid and nonrigid connections have been suggested to overcome this problem, the mechanism of attachment and the ideal connection type remain controversial.^16–19 

Our investigation showed that the implant diameter and length are interrelated with stress distribution in 5 different areas (FPD, mesial implant, distal implant, cancellous bone, and mesial abutment). The 2 factors cannot be interpreted separately from the others. To obtain more reliable and indicative results, the model was idealized as fully as possible. CT scan data from a 40-year-old patient were used to construct the model.

Four operations were performed by this program, the first of which was the thresholding of the assembly. The second was the regional growing of the mandible, the third step was calculating the 3D model, and the fourth was exporting the 3D models to Solidworks. This was followed by the 3D drawing of the model components (implant, periodontal ligament, 3-unit restoration, and premolar). Finally, the 3D components were assembled. In the present study, a substantial mesh was planned; the movement of nodes was limited in the 3 orthogonal directions with no rotation.

Restraints were applied to the bottom and condylar area of 1 side of the mandible; in other words, no translation was allowed for these surfaces in any direction. These restraints were defined to avoid analysis failure due to rigid body motion. The magnitude of VMES at each element, the maximum stress, minimum stress, and the average stress within every part were calculated for each loading condition.

The results of the present study agree with Ding et al²⁰  findings that there is an indirect relationship between the implant diameter and length with the stress and strain on the alveolar crest, but that the relief of stress and strain on the crestal bone is more dependent by the implant width than length. Santiago Junior et al²¹  also explain that increasing the implant width improves the transference of occlusal load to the bone tissues, thus reducing stress under oblique loads. Yeşildal et al²²  state that with applied masticatory force, the increase in implant diameter greatly reduces the VMES values, while increase in implant length increased stress values significantly in both zirconium and titanium implants.

Furthermore, Moriwaki et al²³  assessed the impact of implant length and diameter in addition to bicortical anchorage and they concluded that an implant with a 4-mm width and augmented length should be used to lessen stress on peri-implant cortical bone in cases of sufficient bone quantity. Both de Souza Batista et al²⁴  and Gümrükçü et al²⁵  suggest that implants with increased diameter and length tend to have better stress distribution. Raaj et al²⁶  explain this further, concluding that the approximate force dissipation in the vicinity of implant and bone is affected by implant diameter in cortical bone and implant length in cancellous bone. Augmentation of implant width results in minimum stresses in cortical bone, while increased implant length results in minimum stresses in cancellous bone.

In their recent study, Hamed et al²⁷  conclude that an expansion of implant width combined with a moderate rise in implant length significantly reduced stress beside the stress dissemination around bone. On the other hand, a greater increase in implant length will significantly increase the force distribution on peri-implant bone. Meanwhile, Bordin et al²⁸  note a slight decrease in stress on cortical bone with a rise in implant length. On the other hand, Lemos et al²⁹  declare that no notable changes were observed in force propagation in peri-implant bone using different lengths (7 mm, 8.5 mm, 10 mm). In addition, Memari et al³⁰  report the same findings, wherein the use of different implant lengths produced insignificant variation in force propagation in peri-implant bone; short implants were somehow comparable with long implants.

The outcomes of this research are in accordance with previous studies indicating that force propagation in the implant vicinity relies upon the form and dimensions of the implant.^31–39  In this simulation analysis, the width of the implant is more important for better force dissemination than the implant length. This could be attributed to the uneven distribution of force in bony sockets where the maximum force was placed around the neck; accordingly, forces of mastication are better distributed in implants with wide cervical dimensions (area) (Figure 4).

In the light of these findings, stress can be minimized by a mild increase in implant length. Further augmentation of implant length increases stress, due to the growth of torque. According to our findings, an increase in diameter was directly proportional to the reduction of stress. On the contrary, significant increase in implant length without increase in diameter induced torque and increased stress.

Stress distribution in the bone around any distal implant depends on several factors including diameter, length, the type of prosthetic abutment (either tooth-implant or implant-implant supported). The implant diameter was more important for improved stress distribution than implant length. Moderate increase in the length of the distal implant resulted in a reduction of stress. On the contrary, a significant increase in the length of the distal implant without an increase in diameter induced torque, and increased stress. The optimal combination of distal implant diameter and length was 5.7–10 mm, as it demonstrated the least stress, while the combination of 3.7–10 mm recorded the highest stress and was therefore the least favorable.

Abbreviations

D:

implant diameter

DICOM:

digital imaging communication on medicine

CT:

computed tomography

FEA:

finite element analysis

FPD:

fixed partial denture

L:

implant length

ROI:

Region of interest

VMES:

Von Mises equivalent stress

VMS:

Von Mises equivalent strain

The authors acknowledge Dr Mohamed Bamashmous, Department of Dental Public Health, Faculty of Dentistry, King Abdulaziz University, Jeddah, Saudi Arabia, our independent statistician for his effort in reviewing the methodology and the manuscript.